Question

Select the correct statements from the table.

For each expression, select the true statement in the table.

4x^3 -7x+2
This is a rational expression because the denominator contains a variable.
This is a polynomial with 3 terms.

3x^5+4x-6
This is a rational expression because the denominator contains a variable.
This is a polynomial with 4 terms.

(7x^2+3)(5x+1)
This is a rational expression because the denominator contains a variable. This is a polynomial with 4 terms.

9x^2-6x+1 divided by 5x+7
This is a rational expression because the denominator contains a variable.
This is a polynomial with 3 terms.

8x^4-x^3+6x^2-3x+9
This is a rational expression because the denominator contains a variable.
This is a polynomial with 5 terms.

Answer 1

9x²-6x+1 divided by 5x+7:

This is a rational expression because the denominator contains a variable.

This is a polynomial with 3 terms

Step-by-step explanation:

The only statement that is true is:

9x²-6x+1 divided by 5x+7:

This is a rational expression because the denominator contains a variable.

This is a polynomial with 3 terms.

Variables are represented as 'letters' in mathematics. Since the equation is divided by 5x+7, this shows that the expression is rational i.e a fraction and the denominator 5x+7 contains a variable which is 'x'

The polynomial function here is the function at the numerator i.e 9x²-6x+1 and this contains 3terms. The three terms are 9x², -6x and 1.

Answer 2

Step-by-step explanation:

a)
`4x^3 -7x+2`

This is not a rational expression.

This is a polynomial with 3 terms.

b)
`3x^5+4x-6`

This is not a rational expression because the denominator is constant =1

This is a polynomial with 3 terms.

c)
`(7x^2+3)(5x+1)`

This is not a rational expression because the denominator =1, a constant. This is a polynomial with 4 terms.

d)
`9x^2-6x+1 divided by 5x+7`

This is a rational expression because the denominator contains a variable.

e)
`8x^4-x^3+6x^2-3x+9`

This is not a rational expression because the denominator contains a constant 1

This is a polynomial with 5 terms.